research highlights
A Fast and Robust Linear State Estimator Using Synchronized Phasor Measurements
Despite being widely used, the weighted least squares (WLS) estimator remains to be non-robust, i.e.
estimated states will be inaccurate or grossly biased in the presence of bad measurements. A more robust
and computationally competitive alternative estimator called the least absolute value (LAV) estimator
was investigated. A LAV based “phasor-only” state estimator was developed which has some very unique
advantages when compared to the traditional WLS estimator. This approach is statistically robust since it
will automatically reject gross measurements, eliminate their impact on the estimated state and it is also
computationally efficient due to the linearity of the phasor measurement equations.
The developed estimator was tested using a 3625-bus utility power system, which is measured by only
phasor measurements. The voltage and current phasors are measured at 3800 branches to ensure that the
system is observable and has redundancy in the measurements. Gaussian errors were intentionally added to
all measurements to simulate noisy measurements as would be the case in an actual EMS environment.
Among the many cases tested, three representative cases where there exists (a) no bad data; (b) single bad
data; and (3) five bad data, will be presented. In cases (b) and (c), 100 runs were performed, and errors were
introduced to both voltage and current phasor measurements. Mean squared error (MSE) is computed as
shown below:
The table below provides a comparison of the computational performance of the two estimators for the
above three cases using the average cpu times of the 100 simulations for each case. Simulation CPU times
include the sum of state estimation solution plus bad data processing times for the WLS estimator and the
overall solution time for the LAV estimator. Note the increase in total processing time for the WLS estimator
with an increasing number of bad data versus the relatively fixed computation time for the LAV estimator
which successfully rejected bad data for all cases. While the actual CPU times naturally will depend on the
processor speed and implementation details (here sparse matrix methods are employed, but no effort is put
towards code optimization and simulations are carried out on a commonly used laptop computer), the trend
will remain valid irrespective of these factors.
3625-Bus
Utility System
Simulation
Results
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Dr. Hector A. Pulgar recently joined CURENT’s research
group and the University of Tennessee as an Assistant
Professor. He earned his Ph.D. in Electrical Engineering
from the University of Illinois at Urbana-Champaign in
2010.
Dr. Pulgar’s research interests include power system
dynamics & stability, power system operation & control,
and renewable energy integration.
Welcome, Dr. Pulgar!
newsletter Spring 2014
2